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Natural Logarithm

Define logari...

Question

Define logarithm and write down different properties.

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Solution

Logarithms and Log Properties
$\begin{matrix} D e f i n i t i o n & L o g a r i t h m P r o p e r t i e s y = l o g_{b} x i s e q u i v a l e n t t o x = b^{y} & l o g_{b} b = 1 l o g_{b} 1 = 0 l o g_{b} b^{x} = x b^{b_{g_{a}} x} = x E x a m p l e & l o g_{b} (x^{y}) = r l o g_{b} x l o g_{5} 125 = 3 b e c a u s e 5^{3} = 125 l o g_{b} (x y) = l o g_{b} x + l o g_{b} y S p e c i a l L o g a r i t h m s I n x = l o g_{e} x n a t u r a l l o g & l o g_{b} (\frac{x}{y}) = l o g_{b} x - l o g_{b} y l o g x = l o g_{10} x c o m m o n l o g w h e r e e = 2.718281828 K & T h e d o m a i n o f l o g_{b} x i s x > 0 \end{matrix}$

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